Pythagorean theorem in 3D | Geometry | 8th grade | Khan Academy

TL;DR

Calculate the length of a specific edge in a geometric figure consisting of a rectangular prism and a right pyramid.

Transcript

• [Voiceover] So we have an interesting shape right over here. The base is a rectangular prism. And the dimensions of that rectangular prism, it's three units I guess we could say tall, four units wide, and then four units long. And then on top of that, on top of that, we have what you could call a right pyramid, where the height of this right pyra... Read More

Key Insights

• 🗯️ The figure consists of a rectangular prism and a right pyramid.
• 🇦🇪 The dimensions of the rectangular prism are 3 units tall, 4 units wide, and 4 units long.
• 🗯️ The height of the right pyramid is 1 unit.
• 🦔 The length of one of the edges of the pyramid can be found using the Pythagorean theorem.
• 😥 The rectangular prism helps determine the length of the edge by providing halfway points.
• 🗯️ The length of one side of the pyramid forms a right triangle with the height of 1 unit.
• 🦔 The Pythagorean theorem is applied twice to find the length of the edge.

Questions & Answers

Q: What are the dimensions of the rectangular prism in the figure?

The rectangular prism is 3 units tall, 4 units wide, and 4 units long.

Q: What is the height of the right pyramid in the figure?

The height of the right pyramid is 1 unit.

Q: What is the goal of the problem?

The goal is to determine the length of one of the edges of the pyramid.

Q: Which theorem is used to solve the problem?

The Pythagorean theorem is used to find the length of the edge.

Summary & Key Takeaways

• The figure has a rectangular prism with dimensions 3 units tall, 4 units wide, and 4 units long.

• On top of the rectangular prism is a right pyramid with a height of 1 unit.

• The goal is to find the length of one of the edges of the pyramid.